The present invention is directed to a method of operating a discharge lamp that reduces segregation in the arc discharge tube.
Operation of an arc discharge tube with its axis other than horizontal can lead to segregation of vapor phase species, which in turn leads to color separation over the length of the arc tube, reduced light output, local overheating of the arc tube wall, and other problems that may cause premature lamp failure or unsatisfactory lamp performance. This is particularly true for lamps having high aspect ratio arc tubes (arc tubes whose length-to-width ratio is >about 2).
Acoustic modulation of the input lamp power has been proposed as a solution to the segregation problem. For example, U.S. Pat. No. 6,124,683 describes an arc discharge lamp in which the arc is straightened by acoustic modulation of the lamp power resulting in improved efficacy and a reduced asymmetry of the color. The acoustic modes of discharge lamps are known to those of skill in the art, and the following is a brief summary of what is known. Modulation of lamp power causes modulation of the arc temperature distribution and, as a result, modulation of the gas pressure distribution throughout the arc discharge tube of the lamp. Certain frequencies of modulation cause standing wave oscillation of the gas pressure in the tube. Because of the cylindrical shape of commercial arc discharge tubes, the acoustic modes can generally be described as modes of a cylinder of a size comparable to the discharge, or inner, cavity (i.e., the cavity in which the arc is formed) in the arc tube of the lamp. If the pressure has a spatial dependence along the axis of the tube (i.e., the cylinder of comparable size), then the mode is longitudinal with the number of half-wavelengths in the standing wave determining the order of the mode. For example, if there are two half-wavelengths, the mode is the second longitudinal mode. If the pressure has a spatial dependence along the radius of the tube, then the mode is radial, and if the pressure has a spatial dependence around the circumference of the tube, then the mode is azimuthal. Combination acoustic modes are also possible, such as radial-longitudinal modes and azimuthal-longitudinal modes, in which the pressure distribution varies along more than one coordinate. These combination modes can be further defined, depending on the periodicity of the standing wave, such as a combination acoustic mode of the third azimuthal and second longitudinal modes.
The resonance frequencies for each of these acoustic modes are determined by the dimensions of the discharge cavity of the arc tube and the speed of sound in the gas phase in the discharge cavity. In a first approximation, the speed of sound depends on the arc temperature and the composition of the gas phase in the discharge cavity. More particularly, the speed of sound is proportional to (T/m)1/2 where T is the temperature and m is the average molecular mass of the various vapor phases constituents. In arc tubes having a high Xe gas fill pressure, m is approximately the mass of Xe. Although the arc temperature in an operating arc tube is location dependent, the resonance frequencies nevertheless may be reasonably estimated using an isothermal cylindrical model.
The longitudinal mode (nL) frequencies are roughlyfnL=(n*C)/(2*Length), where fnL is the nth longitudinal mode, C is the average speed of sound in the gas phase, and Length is the cavity length.
The radial mode (nR) frequencies are roughlyfnR=(knR*C)/(π*D) where fnR is the nth radial mode, knR is a constant that is known for each radial mode (it is 3.83 for the first radial mode and higher for subsequent modes), C is the average speed of sound in the gas phase, and D is the diameter of the cavity.
The azimuthal mode (nA) frequencies are roughlyfnA=(knA*C)/(π*D) where fnA is the nth azimuthal mode, knA is a constant that is known for each azimuthal mode (it is 1.84 for the first azimuthal mode, 3.05 for the second, 4.20 for the third and higher for subsequent modes), C is the average speed of sound in the gas phase, and D is the diameter of the cavity.
Better estimates of the resonance frequencies can be obtained from finite element calculations of the eigenmodes of vessels approximating the shape of the cavity in which the arc is formed using well estimated temperature and composition distributions.
For some combination modes the frequencies can be determined by combining the frequencies of the individual modes in quadrature. For example, the resonance frequency of the first radial (1R) and fourth longitudinal (4L) combination mode is:f1RAL2=f1R2=f4L2. 
These frequencies are the power modulation frequencies (denoted herein “power frequencies”). The corresponding voltage (or current) frequencies depend on the type of waveform being applied. For sine waves, the corresponding current (or voltage) frequencies are one-half the power frequencies.
With reference again to the prior art, a further solution to the problem of vertical segregation is offered in U.S. Pat. No. 6,184,633 that suggests that amplitude modulation of an arc-straightening frequency sweep may be effective. For example, a (current) frequency sweep from 45 kHz to 55 kHz every ten milliseconds in a saw tooth pattern may be amplitude modulated at a frequency corresponding to the second longitudinal acoustic mode and a modulation index of 0.24. The modulation index is defined as (Vmax−Vmin)/(Vmax+Vmin), where Vmax is the maximum peak-to-peak voltage of the amplitude modulated envelope and Vmin is the minimum peak-to-peak voltage of the amplitude modulated envelope. This reference points out that amplitude modulation at a frequency corresponding to the first longitudinal acoustic mode is less effective than the preferred frequency corresponding to the second longitudinal acoustic mode, although vertical segregation is reduced somewhat with amplitude modulation at the frequency corresponding to the first longitudinal acoustic mode.